122 Mr. Atwood's Investigations for determining 
the same meaning. Since the balance is in its quiescent posi- 
tion when the index C A is directed to the fixed point O, on 
this account O is called the point of quiescence of the balance, 
or balance spring, indicating the position when the balance is 
not impelled by the spring's elastic force either in one direc- 
tion or the other. If the balance should be turned through 
any angle O C B, the spiral spring being wound through the 
same angle, endeavours by its elastic force to restore itself \ 
and when at liberty, impels the balance through the arc B O 
with an accelerated velocity till it arrives at the position O, 
where the force of acceleration ceases ; with the velocity ac- 
quired at O, the balance proceeds in its vibration, describing 
the arc O E with a retarded motion. 
The elastic forces of the spring at equal distances on the 
opposite sides of the point O, are assumed to be equal ; it is 
also assumed that the effects of friction, and other irregular 
resistances which retard the motion of the balance, are com- 
pensated by the maintaining power, so that the time of de- 
scribing the first arc of vibration BO by an accelerated mo- 
tion, shall be equal to the time of describing the latter arc 
O E by a retarded motion, and that the entire arc of vibra- 
tion BOE is bisected by the point O. 
To render the construction of fig. 1. more distinct, the fixed 
circle O D B E is represented to be at a small distance from 
the circumference of the balance, but is to be considered as co- 
incident with it, so that the arc B O subtending the angle 
B CO, may be of the same length with an arc of the circum- 
ference of the balance which subtends the same angle B C O . 
on this principle CO or C A may be taken indifferently as 
the radius of the balance. 
